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  <div class="section" id="numpy-polynomial-legendre-legendre">
<h1>numpy.polynomial.legendre.Legendre<a class="headerlink" href="#numpy-polynomial-legendre-legendre" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="numpy.polynomial.legendre.Legendre">
<em class="property">class </em><code class="sig-prename descclassname">numpy.polynomial.legendre.</code><code class="sig-name descname">Legendre</code><span class="sig-paren">(</span><em class="sig-param">coef</em>, <em class="sig-param">domain=None</em>, <em class="sig-param">window=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/v1.18.1/numpy/polynomial/legendre.py#L1613-L1653"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numpy.polynomial.legendre.Legendre" title="Permalink to this definition">¶</a></dt>
<dd><p>A Legendre series class.</p>
<p>The Legendre class provides the standard Python numerical methods
‘+’, ‘-‘, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the
attributes and methods listed in the <code class="xref py py-obj docutils literal notranslate"><span class="pre">ABCPolyBase</span></code> documentation.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>coef</strong><span class="classifier">array_like</span></dt><dd><p>Legendre coefficients in order of increasing degree, i.e.,
<code class="docutils literal notranslate"><span class="pre">(1,</span> <span class="pre">2,</span> <span class="pre">3)</span></code> gives <code class="docutils literal notranslate"><span class="pre">1*P_0(x)</span> <span class="pre">+</span> <span class="pre">2*P_1(x)</span> <span class="pre">+</span> <span class="pre">3*P_2(x)</span></code>.</p>
</dd>
<dt><strong>domain</strong><span class="classifier">(2,) array_like, optional</span></dt><dd><p>Domain to use. The interval <code class="docutils literal notranslate"><span class="pre">[domain[0],</span> <span class="pre">domain[1]]</span></code> is mapped
to the interval <code class="docutils literal notranslate"><span class="pre">[window[0],</span> <span class="pre">window[1]]</span></code> by shifting and scaling.
The default value is [-1, 1].</p>
</dd>
<dt><strong>window</strong><span class="classifier">(2,) array_like, optional</span></dt><dd><p>Window, see <a class="reference internal" href="numpy.polynomial.legendre.Legendre.domain.html#numpy.polynomial.legendre.Legendre.domain" title="numpy.polynomial.legendre.Legendre.domain"><code class="xref py py-obj docutils literal notranslate"><span class="pre">domain</span></code></a> for its use. The default value is [-1, 1].</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.6.0.</span></p>
</div>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Methods</p>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.__call__.html#numpy.polynomial.legendre.Legendre.__call__" title="numpy.polynomial.legendre.Legendre.__call__"><code class="xref py py-obj docutils literal notranslate"><span class="pre">__call__</span></code></a>(self, arg)</p></td>
<td><p>Call self as a function.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.basis.html#numpy.polynomial.legendre.Legendre.basis" title="numpy.polynomial.legendre.Legendre.basis"><code class="xref py py-obj docutils literal notranslate"><span class="pre">basis</span></code></a>(deg[, domain, window])</p></td>
<td><p>Series basis polynomial of degree <em class="xref py py-obj">deg</em>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.cast.html#numpy.polynomial.legendre.Legendre.cast" title="numpy.polynomial.legendre.Legendre.cast"><code class="xref py py-obj docutils literal notranslate"><span class="pre">cast</span></code></a>(series[, domain, window])</p></td>
<td><p>Convert series to series of this class.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.convert.html#numpy.polynomial.legendre.Legendre.convert" title="numpy.polynomial.legendre.Legendre.convert"><code class="xref py py-obj docutils literal notranslate"><span class="pre">convert</span></code></a>(self[, domain, kind, window])</p></td>
<td><p>Convert series to a different kind and/or domain and/or window.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.copy.html#numpy.polynomial.legendre.Legendre.copy" title="numpy.polynomial.legendre.Legendre.copy"><code class="xref py py-obj docutils literal notranslate"><span class="pre">copy</span></code></a>(self)</p></td>
<td><p>Return a copy.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.cutdeg.html#numpy.polynomial.legendre.Legendre.cutdeg" title="numpy.polynomial.legendre.Legendre.cutdeg"><code class="xref py py-obj docutils literal notranslate"><span class="pre">cutdeg</span></code></a>(self, deg)</p></td>
<td><p>Truncate series to the given degree.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.degree.html#numpy.polynomial.legendre.Legendre.degree" title="numpy.polynomial.legendre.Legendre.degree"><code class="xref py py-obj docutils literal notranslate"><span class="pre">degree</span></code></a>(self)</p></td>
<td><p>The degree of the series.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.deriv.html#numpy.polynomial.legendre.Legendre.deriv" title="numpy.polynomial.legendre.Legendre.deriv"><code class="xref py py-obj docutils literal notranslate"><span class="pre">deriv</span></code></a>(self[, m])</p></td>
<td><p>Differentiate.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.fit.html#numpy.polynomial.legendre.Legendre.fit" title="numpy.polynomial.legendre.Legendre.fit"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code></a>(x, y, deg[, domain, rcond, full, w, window])</p></td>
<td><p>Least squares fit to data.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.fromroots.html#numpy.polynomial.legendre.Legendre.fromroots" title="numpy.polynomial.legendre.Legendre.fromroots"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fromroots</span></code></a>(roots[, domain, window])</p></td>
<td><p>Return series instance that has the specified roots.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.has_samecoef.html#numpy.polynomial.legendre.Legendre.has_samecoef" title="numpy.polynomial.legendre.Legendre.has_samecoef"><code class="xref py py-obj docutils literal notranslate"><span class="pre">has_samecoef</span></code></a>(self, other)</p></td>
<td><p>Check if coefficients match.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.has_samedomain.html#numpy.polynomial.legendre.Legendre.has_samedomain" title="numpy.polynomial.legendre.Legendre.has_samedomain"><code class="xref py py-obj docutils literal notranslate"><span class="pre">has_samedomain</span></code></a>(self, other)</p></td>
<td><p>Check if domains match.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.has_sametype.html#numpy.polynomial.legendre.Legendre.has_sametype" title="numpy.polynomial.legendre.Legendre.has_sametype"><code class="xref py py-obj docutils literal notranslate"><span class="pre">has_sametype</span></code></a>(self, other)</p></td>
<td><p>Check if types match.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.has_samewindow.html#numpy.polynomial.legendre.Legendre.has_samewindow" title="numpy.polynomial.legendre.Legendre.has_samewindow"><code class="xref py py-obj docutils literal notranslate"><span class="pre">has_samewindow</span></code></a>(self, other)</p></td>
<td><p>Check if windows match.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.identity.html#numpy.polynomial.legendre.Legendre.identity" title="numpy.polynomial.legendre.Legendre.identity"><code class="xref py py-obj docutils literal notranslate"><span class="pre">identity</span></code></a>([domain, window])</p></td>
<td><p>Identity function.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.integ.html#numpy.polynomial.legendre.Legendre.integ" title="numpy.polynomial.legendre.Legendre.integ"><code class="xref py py-obj docutils literal notranslate"><span class="pre">integ</span></code></a>(self[, m, k, lbnd])</p></td>
<td><p>Integrate.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.linspace.html#numpy.polynomial.legendre.Legendre.linspace" title="numpy.polynomial.legendre.Legendre.linspace"><code class="xref py py-obj docutils literal notranslate"><span class="pre">linspace</span></code></a>(self[, n, domain])</p></td>
<td><p>Return x, y values at equally spaced points in domain.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.mapparms.html#numpy.polynomial.legendre.Legendre.mapparms" title="numpy.polynomial.legendre.Legendre.mapparms"><code class="xref py py-obj docutils literal notranslate"><span class="pre">mapparms</span></code></a>(self)</p></td>
<td><p>Return the mapping parameters.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.roots.html#numpy.polynomial.legendre.Legendre.roots" title="numpy.polynomial.legendre.Legendre.roots"><code class="xref py py-obj docutils literal notranslate"><span class="pre">roots</span></code></a>(self)</p></td>
<td><p>Return the roots of the series polynomial.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.trim.html#numpy.polynomial.legendre.Legendre.trim" title="numpy.polynomial.legendre.Legendre.trim"><code class="xref py py-obj docutils literal notranslate"><span class="pre">trim</span></code></a>(self[, tol])</p></td>
<td><p>Remove trailing coefficients</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="numpy.polynomial.legendre.Legendre.truncate.html#numpy.polynomial.legendre.Legendre.truncate" title="numpy.polynomial.legendre.Legendre.truncate"><code class="xref py py-obj docutils literal notranslate"><span class="pre">truncate</span></code></a>(self, size)</p></td>
<td><p>Truncate series to length <em class="xref py py-obj">size</em>.</p></td>
</tr>
</tbody>
</table>
</dd></dl>

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